Dear Professor Insall,
I am afraid you are not being consistent about your
uppercase/lowercase conventions.
If lower case refers to classes only then in the axiom
>PAIR:
>(forall x,y)(thereis z)(forall w)[{[w is in z] iff [(w=x) or (w=y)]}&{[z is
>a set] iff [(x is a set)&(y is a set)]}]
you should probably write thereis Z, for you do not want to a pair of
proper classes to be a class.
Similarly, in
>NCC:
>(forall f){[f is a function] implies (thereis x)[(x is a class) & {(thereis
>y)[y is in x] & [f(x) is not in x]}]}
you should write F for f.
If lower case refers to collections as well as classes then having a pair
of proper collections appartently contradicts your intention to
keep collection in the same relation to classes as classes are to sets.
sincerely,
V.Shavrukov